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Practice Problem: What is the conditional density function
Let (X,Y) be a 2D random variable that is uniformly distributed in the rectangle [1,3]x[5,10].
Find the conditional probability density function
$ f_{X|Y}(x|7). $
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Answer 1
Hint:
- $ f_{XY}(x,y)=\frac{1}{Area \, of \, the \, rectangle} $
- $ f_{X|Y}(x|y) = \frac{f_{XY}(x,y)}{f_{Y}(y)}. $
- $ f_{Y}(y)= \int_{-\infty}^{\infty} f_{XY}(x,y)dx. $
Answer 2
Write it here.
Answer 3
Write it here.
